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 引用本文: 许秩, 范学明. 含裂纹平面问题Erdogan基本解的显式表达[J]. 应用数学和力学, 2017, 38(9): 1009-1020.
XU Zhi, FAN Xue-ming. The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1009-1020. doi: 10.21656/1000-0887.370253
 Citation: XU Zhi, FAN Xue-ming. The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1009-1020.

含裂纹平面问题Erdogan基本解的显式表达

doi: 10.21656/1000-0887.370253

作者简介:许秩（1992—），男，博士生(E-mail: stxuz@163.com);范学明 （1979—），男，讲师，博士(通讯作者. E-mail: fanxm@scut.edu.cn).
• 中图分类号: O343.1

The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks

Funds: The National Natural Science Foundation of China(General Program)(51378009)
• 摘要: 基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件，从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上，对Erdogan基本解的使用条件进行了注解，修正了Erdogan基本解的一些错误，并推导出Erdogan基本解中位移函数解答的显式表达形式.编写了基于Erdogan基本解显式表达的样条虚边界元法（spline fictitious boundary element method, SFBEM）计算程序，计算了具有复合边界条件平面问题的位移、应力和应力强度因子.数值算例结果表明了该文提出的Erdogan基本解显式表达形式的正确性.
•  [1] 郦正能. 应用断裂力学[M]. 北京: 北京航空航天大学出版社, 2012.(LI Zheng-neng. Applied Fracture Mechanics [M]. Beijing: Beihang University Press, 2012.(in Chinese)) [2] Zehnder A T. Fracture Mechanics [M]. Netherlands: Springer, 2012. [3] 付宇明, 田振国, 郑丽娟. 轴对称金属模具电磁热裂纹止裂中热应力场的分析[J]. 应用数学和力学, 2006,27(3): 331-336.(FU Yu-ming, TIAN Zhen-guo, ZHENG Li-juan. Thermal stress field when crack arrest in an axial symmetry metal die using electromagnetic heating[J]. Applied Mathematics and Mechanics,2006,27(3): 331-336.(in Chinese)) [4] Benzley S E. Representation of singularities with isoparametric finite elements[J]. Clinical Endocrinology,1974,8(8): 537-545. [5] Tan M A, Meguid S A. Analysis of bimaterial wedges using a new singular finite element[J]. International Journal of Fracture,1997,88(4): 373-391. [6] MENG Qing-hua, WANG Zhen-qing. Extended finite element method for power-law creep crack growth[J]. Engineering Fracture Mechanics,2014,127: 148-160. [7] Mos N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Methods in Engineering,1999,46(1): 131-150. [8] Portela A, Aliabadi M H, Rooke D P. Dual boundary element incremental analysis of crack propagation[J]. Computers & Structures,1993,46(2): 237-247. [9] Leonel E D, Venturini W S. Dual boundary element formulation applied to analysis of multi-fractured domains[J]. Engineering Analysis With Boundary Elements,2010,34(12): 1092-1099. [10] Erdogan. On the stress distribution in a plate with collinear cuts under arbitrary loads[C]// Proceedings of the 〖STBX〗4th US National Congress of Applied Meehanies . 1962: 547-553. [11] Tan P W, Raju I S, Newman I, et al. Boundary force method for analyzing two-dimensional cracked bodies[R]. Hampton, Virginia: NASA Langley Research Center, 1986. [12] 苏成, 郑淳. 基于Erdogan基本解边界元法计算应力强度因子[J]. 力学学报, 2007,39(1): 93-99.(SU Cheng, ZHENG Chun. Calculation of stress intensity factors by boundary element method based on Erdogan fundamental solutions[J]. Chinese Journal of Theoretical and Applied Mechanics,2007,39(1): 93-99.(in Chinese)) [13] SU Cheng, ZHENG Chun. Probabilistic fracture mechanics analysis of linear-elastic cracked structures by spline fictitious boundary element method[J]. Engineering Analysis With Boundary Elements,2012,36(12): 1828-1837. [14] 吴家龙. 弹性力学[M]. 上海: 同济大学出版社, 2010.(WU Jia-long. Elasticity Mechanics[M]. Shanghai: Tongji University Press, 2010.(in Chinese)) [15] Mogilevskaya S G, Linkov A M. Complex fundamental solutions and complex variables boundary element method in elasticity[J]. Computational Mechanics,1998,22(1): 88-92. [16] Banerjee P K, Butterifeld R. Boundary Element Method in Engineerng Seienee [M]. London: McGraw Hill, 1981. [17] SU Cheng, HAN Da-jian. Multidomain SFBEM and its application in elastic plane problems[J]. Journal of Engineering Mechanics,2000,126(10): 1057-1063.

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出版历程
• 收稿日期:  2016-08-16
• 修回日期:  2017-05-11
• 刊出日期:  2017-09-15

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